Let's divide 42879 by 45
We want to figure out the number of times 42879 can be divided by 45.

Advancing to step 1:
If we divide 4 by 45, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 45

On to step 2:
If we divide 42 by 45, we get 0 and a remainder of 42.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 42 leaves us with 42.
Include the next digit (8) from the dividend after 42, then repeat: 428 / 45

Going ahead to step 3:
45 can be fit into 428 9 times, resulting in a remainder of 23.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
Subtract 405 from 428 to get 23.
Grab the next digit (7) from the dividend, add it to 23, then carry on: 237 / 45

Step 4:
When dividing 237 by 45, we get 5 with a remainder of 12.
The next digit of our result is 5. 
Result so far: 95.0
Deduct 225 from 237 and we're left with 12.
Bring next digit (9) of the dividend behind the 12 and repeat the process: 129 / 45

Step 5:
45 can be fit into 129 2 times, resulting in a remainder of 39.
Write down 2 as next digit of the result. 
Result so far: 952.0
Subtract 90 from 129 to get 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Advancing to step 6:
45 goes into 390 8 times with a remainder of 30.
Write down 8 as next digit of the result. 
Result so far: 952.8
Subtract 360 from 390 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 7:
If we divide 300 by 45, we get 6 and a remainder of 30.
The next digit of our result is 6. 
Result so far: 952.86
If we take 270 away from 300, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
The number 45 fits into 300 6 times, leaving a remainder of 30.
The next digit of our result is 6. 
Result so far: 952.866
Deduct 270 from 300 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 952.866 with a balance of 0.003.